Two cars of the same mass run head-on into each other at C....

Two cars of the same mass run head-on into each other at $C$. After the collision, the cars skid with their brakes locked and come to a stop in the positions shown in the lower part of the figure. Knowing that the speed of car $A$ just before impact was $5 \mathrm{mi} / \mathrm{h}$ and that the coefficient of kinetic friction between the pavement and the tires of both cars is $0.30,$ determine $(a)$ the speed of car $B$ just before impact, $(b)$ the effective coefficient of restitution between the two cars.

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Key Concepts

Coefficient of Restitution

The coefficient of restitution quantifies the elasticity of a collision by comparing the relative speeds after and before impact. It measures how much kinetic energy is conserved in the collision, with a value of 1 indicating a perfectly elastic collision and 0 representing a perfectly inelastic collision.

Work-Energy Principle

The work-energy principle relates the work done by forces (like friction) to the change in kinetic energy of an object. In collision analysis, this principle helps to determine the stopping distances and deceleration of objects after impact.

Conservation of Momentum

This principle states that in an isolated system with no external forces, the total momentum before a collision equals the total momentum after the collision. It is critical for analyzing head?on collisions to determine unknown velocities when two bodies interact.

Kinetic Friction

Kinetic friction is the resistive force acting against the motion of sliding objects. It is characterized by the coefficient of kinetic friction and is responsible for converting kinetic energy into thermal energy during sliding, such as when vehicles come to a stop after a collision.

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